Average Error: 10.9 → 3.2
Time: 2.7s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[x + \frac{\frac{y}{a - t}}{\frac{1}{z - t}}\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
x + \frac{\frac{y}{a - t}}{\frac{1}{z - t}}
double code(double x, double y, double z, double t, double a) {
	return (x + ((y * (z - t)) / (a - t)));
}
↓
double code(double x, double y, double z, double t, double a) {
	return (x + ((y / (a - t)) / (1.0 / (z - t))));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original10.9
Target1.3
Herbie3.2
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Initial program 10.9

    \[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
  2. Using strategy rm

  3. Applied associate-/l*1.3

    \[\leadsto x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}}\]
  4. Using strategy rm

  5. Applied div-inv1.4

    \[\leadsto x + \frac{y}{\color{blue}{\left(a - t\right) \cdot \frac{1}{z - t}}}\]

  6. Applied associate-/r*3.2

    \[\leadsto x + \color{blue}{\frac{\frac{y}{a - t}}{\frac{1}{z - t}}}\]

  7. Final simplification3.2

    \[\leadsto x + \frac{\frac{y}{a - t}}{\frac{1}{z - t}}\]

Reproduce

herbie shell --seed 2020078 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- a t) (- z t))))

  (+ x (/ (* y (- z t)) (- a t))))